[Formerly: Publ. I.R.M.A. Strasbourg, 1982, 182/S-04, p. 59-78.]

First, the two theorems by Euler and Seidel are stated and further applied to various examples. The most striking examples are those in which the Euler-Seidel matrix provides a rapid calculation of the initial sequence of integers that have themselves a combinatorial interpretation. For each example we give the sequence of the first values according to a principle dear to the enumerating practitioners.

Département de mathématique, Université Louis Pasteur, Strasbourg

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